Abstract
In this work, we focus on an initial value problem for a class of 2D time-fractional diffusion evolution equations with Riemann–Liouville fractional derivative. There are three new results in this paper. First of all, the existence and ill-posedness result (in the sense of Hadamard) in three cases which are consisting of homogeneous, inhomogeneous, and nonlinear problems are considered. Next, by using the Fourier truncation method, we show that regularized problems are well-posed. Finally, some demonstrated examples are presented to test the proposed method.
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